Final answer:
The expression 18x³yA - 39x⁴y³ is factored by first finding the GCF, which is 3x³y. The correct factored form is 3x³y(6A - 13x¹y²), so the answer is option B.
Step-by-step explanation:
To factor completely the expression 18x³yA - 39x⁴y³, we need to find the greatest common factor (GCF) of the terms. Both terms have an x³ and a y in common, and the numerical coefficients 18 and 39 have a greatest common factor of 3. Therefore, the GCF is 3x³y. Factoring this out of the expression gives us:
3x³y(6A - 13x¹y²)
Now, we inspect our answer options:
- A. 3x³y(6A - 13x)
- B. 3x³y(6 - 13x³y²)
- C. 3x³y(6 - 13x²y³)
- D. 3x³y(6 - 13xy)
By carefully comparing the factored expression and the options, we see that option B is the correct answer. The factored expression should have a -13x multiplier on the y², which is only present in option B.